Interactively exploring elimination orderings in symbolic sparse Cholesky factorization.

Abstract

When large sparse symmetric systems of linear equations are solved by the Cholesky factorization, nonzero elements can be generated at positions where the original matrix contains zero elements. This phenomenon is called fill-in and it is often crucial in large-scale problems. The symbolic Cholesky factorization solely takes into account the nonzero structure of a sparse matrix to determine the nonzero structure of its Cholesky factor. Sequences of elimination graphs are typically used to model this combinatorial problem. We propose an interactive educational module to visualize and explore the symbolic Cholesky factorization in terms of both elimination graphs and matrix representation. We describe the design and implementation of this interactive module that is intended to be used in a face-to-face learning environment.